On known machines of this type, the skirts are deformed by centrifugal force during work. They then have a tendency to be pulled away from the ground, which brings about a poor gathering of the products to be moved and causes losses. Moreover, the outside part of the skirts wears rather quickly and even tears because of rubbing on the ground and as a result of encounters with obstacles such as stones or stumps on the ground. Because of these defects, the quality of the work obtained with these skirts is obviously reduced, especially with regard to the neatness of the gathering. Because of this, the user can be led rather quickly to change the skirts.